The potential \(V(x)\)  has been considered earlier in the context of
single component local[1]} as well as non-local[2]} NLSE.
The nonlinear strengths \(g_{ij}\) 's may be tailored for the above \(f(x)\)  satisfying
\(\frac{1}{2} (f_1(x)+f_2(x))=f(x)\) .
Following the discussions in Appendix-I, the sum of the roots \(Q_1,Q_2,Q_3\)  is zero
for \(m=0\) , implying that all three roots can not either be positive or negative. We choose \(Q_1 <0,Q_2 >0, Q_3 >0\) . The solution of Eq.(REF ) for \(\sigma =-1\)  is obtained as,
\(u(\zeta ) = \sqrt{Q_3 - (Q_3 - Q_2) sn^2(\lambda \zeta ,r)}\) 
